This invention relates to a device and method for mixing substances, particularly very viscous substances in small volumes.
The mixing of liquids is essential for many industrial and laboratory processes, and has been addressed in the past, for example in the following publications:
(1) Shraiman, B. I. and Siggia, E. D. Scalar turbulence, Nature, 405, 639-545 (2000).
(2) Warhaft, Z., Passive scalars in turbulent flows Annu. Rev. Fluid Mech. 32, 203-240 (2000).
Since the process of molecular diffusion is typically characterized by a long characteristic time, rapid mixing almost always requires some macroscopic flow, which is regularly induced by stirring or shaking. In order to provide efficient mixing, however, the flow needs to be chaotic or turbulent. It is known that a flow is likely to be turbulent, when the Reynolds number, Re, is large (Re=VL/xcexd, wherein V is the liquid velocity, L is the size of a tank in which the liquid flows, and xcexd is the kinematic viscosity of the liquid). Thus, in order to obtain a high Reynolds number, the liquid velocity and the tank size should be sufficiently large while the liquid should be of low viscosity. When the liquids are very viscous and/or the tank is small, the velocity required to create a turbulent flow may be so high, that it becomes quite impractical. In this case, liquids arc usually mixed in closed mixers. However, this interrupts the continuous technological processes and requires a lot of energy to provide a homogeneous mixture.
It is known that solutions of flexible high molecular weight polymers differ from newtonian fluids in many aspects. The most notable elastic property of the polymer solution is that stress does not immediately become zero, when the fluid motion stops, but rather decays with some characteristic time, xcex, which can reach seconds and even minutes. The equation of motion for dilute polymer solutions differs from the Navier-Strokes equation defining the motion of simple, low molecular weight newtonian fluids by an additional linear term arising from the elastic stress. Since the elastic stress is caused by stretching of the polymer coils, it depends on history of motion and deformations of fluid elements along their flow trajectories. This implies a nonlinear relationship between the elastic stress and the rate of strain in the flow. These features can be learned from the following publication:
(3) Bird, R. B., Curtiss, C. F., Armstrong, R. C. and Hassager, O., Dynamics of polymeric liquids, John Wiley, NY, 1987.
The non-linear mechanical properties of viscoelastic fluids can lead to many special flow effects, such as purely elastic transitions that quantitatively change character of the flow at vanishingly small Reynolds number. This is disclosed in the following publications:
(4) R. G. Larson et al., xe2x80x9cA Purely Viscoelastic Instability in Taylor-Couette Flowxe2x80x9d, J. Fluid Mech., 218, 573-600, 1990;
(5) Byars, J. A., xc3x96ztekin, A., Brown R. A. and McKinley, G. H., Spiral instabilities in the flow of highly elastic fluids between rotating parallel disks, J. Fluid Mech., 271, 173-218 (1994).
(6) Joo, J. L. and Shaqfeh., E. S. G., Observations of purely elastic instabilities in the Taylor-Dean flow of a Boger fluid, J. Fluid Mech 262, 27-73 (1994).
As a result of such transitions, secondary vortical flow appears in different systems, where the primary motion is a curvilinear shear flow. The onset of those secondary flows depends on the Weissenberg number, Wi, determined as Wi=xcexxcex3, wherein xcex is the polymer relaxation time, and xcex3 is the shear rate. The Weissenberg number plays a role analogous to that of the Reynolds number in competition between non-linearity and dissipation.
There is a need in the art to facilitate the mixing of substances, by providing a novel method and device that enables the efficient mixing of substances even very viscous, in small volumes, at arbitrary low Reynolds numbers. The present invention provides for the gentle mixing of viscous liquids in small size channels at low velocities and small applied stresses, as well as mixing between a viscous liquid and a powder.
It has been found by the inventors that the flow of a sufficiently elastic polymer solution can become very irregular even at low velocity, high viscosity, and in a small volume (tank). The fluid motion is excited in a broad range of spatial and temporal scales, and the flow resistance significantly increases (by a factor up to twenty), thereby presenting a turbulent flow. These main features of turbulence appear in a flow of a highly elastic polymer solution, even at arbitrarily low Reynolds numbers. A comparable state of turbulent flow for a newtonian fluid in a pipe would have a Reynolds number as high as 105.
The inventors have found that the nonlinearity of mechanical properties of a fluid can give rise to a turbulent flow when the equation of motion is linear. For a polymer solution, this corresponds to a state in which the Weissenberg number is high, while the Reynolds number is small. This situation can be realized if the parameter of elasticity, Wi/Re=xcexxcexd/L2, is large enough, wherein L is characteristic size and xcexd is kinematic viscosity of the fluid.
The main idea of the present invention is based on the creation of turbulence in a liquid (even very viscous liquid) in a flow with curvilinear trajectories, by adding a small amount of polymer. This can be used for mixing this liquid with another substance (liquid or powder). The flow of an elastic polymer solution at sufficiently high values of Weissenberg number, Wi, has all the main features of the developed turbulence. The increase in the flow resistance resulting in the turbulence of the flow is due to the elastic stress provided by the presence of a polymer material.
There is thus provided according to one aspect of the present invention a method of creating a turbulent flow of a liquid, the method comprising the step of providing a polymer material in the liquid flow with curvilinear trajectories.
For the purposes of the present invention, the presence of a polymer material of at least 0.001% concentration is sufficient. Preferably, the polymer material is a flexible high molecular weight polymer.
The above technique can be used for effective mixing of the liquid with another substance (liquid or powder). The efficient mixing can be carried out at arbitrary small Reynolds numbers.
According to another aspect of the present invention, there is provided a method of mixing substances, at least one of the substances being a liquid, the method comprising the steps of:
(i) providing a continuous flow of the substances with curvilinear trajectories of the flow: and
(ii) providing a polymer material in the liquid flow, thereby creating turbulence of the flow.
To provide effective mixing of the substances, the flow periodically turns, resulting in that the difference in the concentration of the substances in the flow exponentially reduces. A characteristic length of the path defining effective mixing of the substances is preferably such that this difference reduces by about 3 times.
According to some embodiments of the invention, the curvilinear trajectories of the flow are achieved by directing the flow along a serpentine- or worm-like channel, so as to provide an open continuous flow of the substances through the channel between inlet and outlet openings thereof. According to another embodiment of the invention, the curvilinear trajectories of the flow are achieved by circulating the substances in a cylindrically shaped mixing tank. Such a tank defines a closed continuous flow of the substances with the curvilinear trajectories of the flow.
According to yet another aspect of the present invention, there is provided a mixing device for mixing substances, at least one of the substances being a liquid, the mixing device comprising:
(a) a mixing tank for a flow of the substances therein with curvilinear trajectories of the flow; and
(b) a supply means for supplying the substances into the tank with presence of a polymer material in the liquid flow.